Chech Device Manager first and see if you have a WWAN card and check its compatible carrier. Insert a SIM Card with that specific carrier. Personally, I wouldnt use it.

Welcome to the jungle, we have FrankenPads
If you want it you're going to bleed, but that is the price to pay
And you're a very rare mobo, very hard to get
You can see the blinky lights, but you won't get them for free.

It has a Sierra Wireless MC8775 HSDPA modem. Now what program should I use to connect to my ISP?

I'm fairly certain that these were locked to Vodafone in your country, so you need to give them a call, see if the card is still supported by their network and purchase a plan.

I came across a communications program from Lenovo - Access Connections (Fn+F5) which showed a number of comms interfaces one of which was Mobile Broadband, This told me that no SIM card was present Insert SIM card and try again. Then I reinserted it the other way round as their is no indication as to which way round it should be inserted. Of course it made no difference, the same error msg came up. I would have thought that if it was locked then some other msg would have been displayed BICBW.
I later came across something called 'Lenovo Broadband Activation for Windows':-

my answer here would be a bit inappropriate, but I still want to give you an advise.
Get some modern WWAN card and get rid of that outdated card.
Not only you will get a better speeds and connectivity, but also you will face a lot less problems with the installation.
X61 does support a wide range of Sierra's cards and there's just no point in using such old card.
I would personally recommend either MC7710 or MC7455 card. Both are LTE-capable modems.

As for your card I can say this:
I remember time when I was using a GOBI3000 card. And I had to use an utility called GobiAllPowerSwitcher.
I had to change something in that card with this utility. After this I was able to see a Carrier network in the
Windows Wireless Menu. Maybe this utility will help you with your card (I guess it's GOBI2000).

Thanks for your advice. I would like to have 4G capability and will probably get an MC7710 card, but the immediate problem is being able to access a provider. At the moment I get error msgs saying there is no SIM card, and I don't know if this is because of a misconfiguration or hardware problem. If I can't get this sorted I can't imagine replacing the card would provide any benefit.

Thanks for your advice. I would like to have 4G capability and will probably get an MC7710 card, but the immediate problem is being able to access a provider. At the moment I get error msgs saying there is no SIM card, and I don't know if this is because of a misconfiguration or hardware problem. If I can't get this sorted I can't imagine replacing the card would provide any benefit.

Two things here:

1) The machine likely shipped with a "dummy" SIM card. You need a *real* Vodafone SIM in order to activate and use its WWAN capability. I'll repeat myself for the last time regarding this particular issue: give Vodafone a call.

2) You will also need a modded BIOS installed in order for the system not to "bark" at the newer card and prevent the machine from booting altogether.

...Knowledge is a deadly friend when no one sets the rules...(King Crimson)

For anyone who has an X61 with WWAN capability via a Sierra Wireless MC8775 card, I'd suggest upgrading the firmware which will enable it to work at 7.2 Mb/s which is twice as fast as it is originally. Also it will no longer be locked so you can use any SIM, and it will work on Linux and FreeBSD as well as Windows.

Thanks for your advice. I would like to have 4G capability and will probably get an MC7710 card, but the immediate problem is being able to access a provider. At the moment I get error msgs saying there is no SIM card, and I don't know if this is because of a misconfiguration or hardware problem. If I can't get this sorted I can't imagine replacing the card would provide any benefit.

Two things here:

1) The machine likely shipped with a "dummy" SIM card. You need a *real* Vodafone SIM in order to activate and use its WWAN capability. I'll repeat myself for the last time regarding this particular issue: give Vodafone a call.

No need to call Vodafone - just upgrade firmware then use any SIM card you like.

1) The machine likely shipped with a "dummy" SIM card. You need a *real* Vodafone SIM in order to activate and use its WWAN capability.

True, I believe my T61p has a dummy red sim card (fools me into thinking it's a Vodafone card)... Either that or card is expired. Echoing George's advice + why don't you just go to a Vodafone store and buy a $2 sim to see if receives reception.

The other user suggested a new WWAN card, but 4G cards are quite expensive, so better to see if your existing card works first. A new card might entail a BIOS flash as well.

1) The machine likely shipped with a "dummy" SIM card. You need a *real* Vodafone SIM in order to activate and use its WWAN capability.

True, I believe my T61p has a dummy red sim card (fools me into thinking it's a Vodafone card)... Either that or card is expired. Echoing George's advice + why don't you just go to a Vodafone store and buy a $2 sim to see if receives reception.

I did buy a Vodafone SIM and it did work, but after upgrading the firmware I have doubled the speed and am no longer locked to Vodafone.